A continuous function has a graph without gaps, splits, or holes. [This video explains how to find the continuity and discontinuity at a point from a graph of the function.
Playlist: https://www.youtube.com/watch?v=6Y4uTTgp938&list=PLxLfqK5kuW7Qc5n8RbJYqUBXo_IqcBJyN
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Continuity 2.4: Checking the continuity from a graph | NatokHD